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Number of ways to write n as an ordered sum of 3 nonzero tetrahedral numbers.
8

%I #7 Feb 20 2021 07:53:56

%S 1,0,0,3,0,0,3,0,0,4,0,0,6,0,0,3,0,0,3,3,0,3,6,0,0,3,0,1,6,0,0,6,0,0,

%T 3,0,0,9,3,0,3,3,0,6,0,0,6,3,0,0,0,0,3,6,0,3,6,1,6,0,0,3,6,0,6,0,0,6,

%U 3,0,0,3,3,3,6,0,0,9,0,0,0,0,0,9,0,0,6,3,0,9,0,0,12

%N Number of ways to write n as an ordered sum of 3 nonzero tetrahedral numbers.

%F G.f.: ( Sum_{k>=1} x^binomial(k+2,3) )^3.

%t nmax = 95; CoefficientList[Series[Sum[x^Binomial[k + 2, 3], {k, 1, nmax}]^3, {x, 0, nmax}], x] // Drop[#, 3] &

%Y Cf. A000292, A023533, A023670, A053604, A282582, A341774, A341795, A341796, A341797.

%K nonn

%O 3,4

%A _Ilya Gutkovskiy_, Feb 19 2021